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If the controller in which the PSR constraint is assigned to does not already match the position or rotation of the joint then you must use the feature called Maintain Original in the offset tab of the PSR constraint, this is the only thing that will distort the mesh under them conditions. Any other distortion is down to weighting.

Looking at the images again I see your refering to the bottom outer teeth pointing in slightly. I deleted all constraints and see the bottom outer teeth are indeed still pointing in so this is not a constraint issue. When I first looked at the file I thought you intended the bottom teeth to be different slightly to the top and was looking for fault in the whole movement of the teeth which works fine.

If you turn off the skin and the mesh returns to its correct shape then its a weighting issue. If you get the weight paint tool and put it to smooth and brush over them verts that are out your see them move. Look at the file I quickly done this too. I only had seconds to do it but your see its a weighting issue.

The other confusing things is as to why you need two joints for the teeth, do you intend on bending them at some point? The teeth just needs to be weighted to the head for the upper teeth, and the jaw for lower teeth. You do do this all you need to do is weight the selected teeth 100% where there is no room for error. Normaly teeth dont have constraints to them but assume you are doing this for a reason. Again if in any doubt what the distortion issue is turn off the skin object and if the issue goes away you have weighting issues. If the object as a whole changes orientation or position when you apply a constraint then its because the controller does not match the PSR of the joint in which case you use Maintain Original from the constraints tab settings.